Novel Nanotube Multiquantum Dot Devices.

Addressable quantum states well isolated from the environment are of considerable interest for quantum information science and technology. Carbon nanotubes are an appealing system, since a perfect crystal can be grown without any missing atoms and its cylindrical structure prevents ill-defined atomic arrangement at the surface. Here, we develop a reliable process to fabricate compact multielectrode circuits that can sustain the harsh conditions of the nanotube growth. Nanotubes are suspended over multiple gate electrodes, which are themselves structured over narrow dielectric ridges to reduce the effect of the charge fluctuators of the substrate. We measure high-quality double- and triple-quantum dot charge stability diagrams. Transport measurements through the triple-quantum dot indicate long-range tunneling of single electrons between the left and right quantum dots. This work paves the way to the realization of a new generation of condensed-matter devices in an ultraclean environment, including spin qubits, mechanical qubits, and quantum simulators.

Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers.

We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65) ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

Fabry-Pérot Oscillations in Correlated Carbon Nanotubes.

We report the observation of an intriguing behavior in the transport properties of nanodevices operating in a regime between the Fabry-Pérot and the Kondo limits. Using ultrahigh quality nanotube devices, we study how the conductance oscillates when sweeping the gate voltage. Surprisingly, we observe a fourfold enhancement of the oscillation period upon decreasing temperature, signaling a crossover from single-electron tunneling to Fabry-Pérot interference. These results suggest that the Fabry-Pérot interference occurs in a regime where electrons are correlated. The link between the measured correlated Fabry-Pérot oscillations and the SU(4) Kondo effect is discussed.

Mass Sensing for the Advanced Fabrication of Nanomechanical Resonators.

We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam-induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detection method is highly effective as it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, this method is simple to use and readily available to a wide range of potential users because it can be operated in existing commercial FEBID systems without making any modification. The presented method allows one to engineer hybrid nanomechanical resonators with precisely tailored functionalities. It also appears as a new tool for studying the growth dynamics of ultrathin nanostructures, opening new opportunities for investigating so far out-of-reach physics of FEBID and related methods.

Landau Velocity for Collective Quantum Hall Breakdown in Bilayer Graphene.

Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter-Landau-level (LL) Zener field, the ratio of the Landau gap and the cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large super-Poissonian shot noise signals the breakdown via inter-LL scattering. The breakdown is ultimately limited by collective excitations in a regime where phonon and impurity scattering are quenched. The breakdown mechanism can be described by a Landau critical velocity as it bears strong similarities with the roton mechanism of superfluids. In addition, we show that breakdown is a precursor of an electric-field induced QHE-metal transition.

Ultrasensitive Displacement Noise Measurement of Carbon Nanotube Mechanical Resonators.

Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultralight resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultrasensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to ∼150 nm. These advances in detection and fabrication allow us to reach [Formula: see text] displacement sensitivity. Thermal vibrations cooled cryogenically at 300 mK are detected with a signal-to-noise ratio as high as 17 dB. We demonstrate [Formula: see text] force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is an important step toward imaging individual nuclear spins and studying the coupling between mechanical vibrations and electrons in different quantum electron transport regimes.

Optomechanics with a hybrid carbon nanotube resonator.

In just 20 years of history, the field of optomechanics has achieved impressive progress, stepping into the quantum regime just 5 years ago. Such remarkable advance relies on the technological revolution of nano-optomechanical systems, whose sensitivity towards thermal decoherence is strongly limited due to their ultra-low mass. Here we report a hybrid approach pushing nano-optomechanics to even lower scales. The concept relies on synthesising an efficient optical scatterer at the tip of singly clamped carbon nanotube resonators. We demonstrate high signal-to-noise motion readout and record force sensitivity, two orders of magnitude below the state of the art. Our work opens the perspective to extend quantum experiments and applications at room temperature.

High Quality Factor Graphene-Based Two-Dimensional Heterostructure Mechanical Resonator.

Ultralight mechanical resonators based on low-dimensional materials are well suited as exceptional transducers of minuscule forces or mass changes. However, the low dimensionality also provides a challenge to minimize resistive losses and heating. Here, we report on a novel approach that aims to combine different two-dimensional (2D) materials to tackle this challenge. We fabricated a heterostructure mechanical resonator consisting of few layers of niobium diselenide (NbSe2) encapsulated by two graphene sheets. The hybrid membrane shows high quality factors up to 245,000 at low temperatures, comparable to the best few-layer graphene mechanical resonators. In contrast to few-layer graphene resonators, the device shows reduced electrical losses attributed to the lower resistivity of the NbSe2 layer. The peculiar low-temperature dependence of the intrinsic quality factor points to dissipation over two-level systems which in turn relax over the electronic system. Our high sensitivity readout is enabled by coupling the membrane to a superconducting cavity which allows for the integration of the hybrid mechanical resonator as a sensitive and low loss transducer in future quantum circuits.

Real-Time Measurement of Nanotube Resonator Fluctuations in an Electron Microscope.

Mechanical resonators based on low-dimensional materials provide a unique platform for exploring a broad range of physical phenomena. The mechanical vibrational states are indeed extremely sensitive to charges, spins, photons, and adsorbed masses. However, the roadblock is often the readout of the resonator, because the detection of the vibrational states becomes increasingly difficult for smaller resonators. Here, we report an unprecedentedly sensitive method to detect nanotube resonators with effective masses in the 10-20 kg range. We use the beam of an electron microscope to resolve the mechanical fluctuations of a nanotube in real-time for the first time. We obtain full access to the thermally driven Brownian motion of the resonator, both in space and time domains. Our results establish the viability of carbon nanotube resonator technology at room temperature and pave the way toward the observation of novel thermodynamics regimes and quantum effects in nanomechanics.

Force sensitivity of multilayer graphene optomechanical devices.

Mechanical resonators based on low-dimensional materials are promising for force and mass sensing experiments. The force sensitivity in these ultra-light resonators is often limited by the imprecision in the measurement of the vibrations, the fluctuations of the mechanical resonant frequency and the heating induced by the measurement. Here, we strongly couple multilayer graphene resonators to superconducting cavities in order to achieve a displacement sensitivity of 1.3 fm Hz(-1/2). This coupling also allows us to damp the resonator to an average phonon occupation of 7.2. Our best force sensitivity, 390 zN Hz(-1/2) with a bandwidth of 200 Hz, is achieved by balancing measurement imprecision, optomechanical damping, and measurement-induced heating. Our results hold promise for studying the quantum capacitance of graphene, its magnetization, and the electron and nuclear spins of molecules adsorbed on its surface.

Nanotube mechanical resonators with quality factors of up to 5 million.

Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surfaces, and the pristine electronic states they host. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here, we observe quality factors Q as high as 5 × 10(6) in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define Q as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires the use of an ultra-low-noise method to rapidly detect minuscule vibrations, as well as careful reduction of the noise of the electrostatic environment. We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. We measure record-high quality factors, which are comparable to the highest Q values reported in mechanical resonators of much larger size, a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low mass and very large Q offers new opportunities for ultra-sensitive detection schemes and quantum optomechanical experiments.

Atomic monolayer deposition on the surface of nanotube mechanical resonators.

We study monolayers of noble gas atoms (Xe, Kr, Ar, and Ne) deposited on individual ultraclean suspended nanotubes. For this, we record the resonance frequency of the mechanical motion of the nanotube, since it provides a direct measure of the coverage. The latter is the number of adsorbed atoms divided by the number of the carbon atoms of the suspended nanotube. Monolayers form when the temperature is lowered in a constant pressure of noble gas atoms. The coverage of Xe monolayers remains constant at 1/6 over a large temperature range. This finding reveals that Xe monolayers are solid phases with a triangular atomic arrangement, and are commensurate with the underlying carbon nanotube. By comparing our measurements to theoretical calculations, we identify the phases of Ar and Ne monolayers as fluids, and we tentatively describe Kr monolayers as solid phases. These results underscore that mechanical resonators made from single nanotubes are excellent probes for surface science.

Coupling graphene mechanical resonators to superconducting microwave cavities.

Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies, quality factors, and low mass. An outstanding challenge, however, has been to obtain large coupling between the motion and external systems for efficient readout and manipulation. Here, we report on a novel approach, in which we capacitively couple a high-Q graphene mechanical resonator (Q ≈ 10(5)) to a superconducting microwave cavity. The initial devices exhibit a large single-photon coupling of ∼10 Hz. Remarkably, we can electrostatically change the graphene equilibrium position and thereby tune the single photon coupling, the mechanical resonance frequency, and the sign and magnitude of the observed Duffing nonlinearity. The strong tunability opens up new possibilities, such as the tuning of the optomechanical coupling strength on a time scale faster than the inverse of the cavity line width. With realistic improvements, it should be possible to enter the regime of quantum optomechanics.

Interplay of driving and frequency noise in the spectra of vibrational systems.

We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.

Imaging the proton concentration and mapping the spatial distribution of the electric field of catalytic micropumps.

Catalytic engines can use hydrogen peroxide as a chemical fuel in order to drive motion at the microscale. The chemo-mechanical actuation is a complex mechanism based on the interrelation between catalytic reactions and electro-hydrodynamics phenomena. We studied catalytic micropumps using fluorescence confocal microscopy to image the concentration of protons in the liquid. In addition, we measured the motion of particles with different charges in order to map the spatial distributions of the electric field, the electrostatic potential and the fluid flow. The combination of these two techniques allows us to contrast the gradient of the concentration of protons against the spatial variation in the electric field. We present numerical simulations that reproduce the experimental results. Our work sheds light on the interrelation between the different processes at work in the chemomechanical actuation of catalytic pumps. Our experimental approach could be used to study other electrochemical systems with heterogeneous electrodes.

Symmetry breaking in a mechanical resonator made from a carbon nanotube.

Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.

Ultrasensitive force detection with a nanotube mechanical resonator.

Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, including the dynamics of individual electron spins, persistent currents in normal metal rings and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN Hz(-1/2) at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultrasensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. This detection method also allows us to measure the Brownian vibrations of the nanotube down to cryogenic temperatures. Force sensing with nanotube resonators offers new opportunities for detecting and manipulating individual nuclear spins as well as for magnetometry measurements.

Strong coupling between mechanical modes in a nanotube resonator.

We report on the nonlinear coupling between the mechanical modes of a nanotube resonator. The coupling is revealed in a pump-probe experiment where a mode driven by a pump force is shown to modify the motion of a second mode measured with a probe force. In a second series of experiments, we actuate the resonator with only one oscillating force. Mechanical resonances feature exotic line shapes with reproducible dips, peaks, and jumps when the measured mode is commensurate with another mode with a frequency ratio of either 2 or 3. Conventional line shapes are recovered by detuning the frequency ratio using the voltage on a nearby gate electrode. The exotic line shapes are attributed to strong coupling between the mechanical modes. The possibility to control the strength of the coupling with the gate voltage holds promise for various experiments, such as quantum manipulation, mechanical signal processing, and the study of the quantum-to-classical transition.

A nanomechanical mass sensor with yoctogram resolution.

Nanomechanical resonators have been used to weigh cells, biomolecules and gas molecules, and to study basic phenomena in surface science, such as phase transitions and diffusion. These experiments all rely on the ability of nanomechanical mass sensors to resolve small masses. Here, we report mass sensing experiments with a resolution of 1.7 yg (1 yg = 10(-24) g), which corresponds to the mass of one proton. The resonator is a carbon nanotube of length ∼150 nm that vibrates at a frequency of almost 2 GHz. This unprecedented level of sensitivity allows us to detect adsorption events of naphthalene molecules (C(10)H(8)), and to measure the binding energy of a xenon atom on the nanotube surface. These ultrasensitive nanotube resonators could have applications in mass spectrometry, magnetometry and surface science.

Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene.

The theory of damping is discussed in Newton's Principia and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes and graphene sheets. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.